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Tan, Bing; Liu, Liya; Qin, Xiaolong

Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems. (English) Zbl 07378248

Japan J. Ind. Appl. Math. 38, No. 2, 519-543 (2021).
Summary: We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.

Cited in 17 Documents

MSC:

47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65K15 Numerical methods for variational inequalities and related problems

Keywords:

inertial subgradient extragradient method; inertial Tseng’s extragradient method; steepest descent method; bilevel variational inequality problem; pseudomonotone mapping

Software:

FOM
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Full Text: DOI

References:

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